From Firm Productivity Dynamics

to Aggregate E�ciency

Bernabe Lopez-MartinBanco de México

ABCDE Conference �Productivity, Growth, and the Law�Mexico City, June 15-16 2015

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Disclaimer

The views expressed in this presentation are exclusively those of theauthor and do not necessarily represent those of Banco de Mexico.

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Introduction

TFP largely accounts for cross-country GDP per capita di�erences.

(e.g. Caselli, 2005: capital + human capital explains <50% crosscountry income per capita)

Part of these TFP di�erences have been attributed to:

• Larger dispersion of marginal product of capital and laboracross �rms in developing economies, misallocation.

I Evidence found in many countries: Hsieh & Klenow (2009),Busso, Madrigal & Pages (2012).

I For example: reducing dispersion across manufacturing plantsin Mexico to level of US implies a TFP gain of approx. 50%.

• Lower growth of productivity at the �rm level (Hsieh &Klenow, 2014).

What models (and frictions) can explain these observations?

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Introduction

TFP largely accounts for cross-country GDP per capita di�erences.(e.g. Caselli, 2005: capital + human capital explains <50% crosscountry income per capita)

Part of these TFP di�erences have been attributed to:

• Larger dispersion of marginal product of capital and laboracross �rms in developing economies, misallocation.

I Evidence found in many countries: Hsieh & Klenow (2009),Busso, Madrigal & Pages (2012).

I For example: reducing dispersion across manufacturing plantsin Mexico to level of US implies a TFP gain of approx. 50%.

• Lower growth of productivity at the �rm level (Hsieh &Klenow, 2014).

What models (and frictions) can explain these observations?

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Introduction

TFP largely accounts for cross-country GDP per capita di�erences.(e.g. Caselli, 2005: capital + human capital explains <50% crosscountry income per capita)

Part of these TFP di�erences have been attributed to:

• Larger dispersion of marginal product of capital and laboracross �rms in developing economies, misallocation.

I Evidence found in many countries: Hsieh & Klenow (2009),Busso, Madrigal & Pages (2012).

I For example: reducing dispersion across manufacturing plantsin Mexico to level of US implies a TFP gain of approx. 50%.

• Lower growth of productivity at the �rm level (Hsieh &Klenow, 2014).

What models (and frictions) can explain these observations?

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Introduction

TFP largely accounts for cross-country GDP per capita di�erences.(e.g. Caselli, 2005: capital + human capital explains <50% crosscountry income per capita)

Part of these TFP di�erences have been attributed to:

• Larger dispersion of marginal product of capital and laboracross �rms in developing economies, misallocation.

I Evidence found in many countries: Hsieh & Klenow (2009),Busso, Madrigal & Pages (2012).

I For example: reducing dispersion across manufacturing plantsin Mexico to level of US implies a TFP gain of approx. 50%.

• Lower growth of productivity at the �rm level (Hsieh &Klenow, 2014).

What models (and frictions) can explain these observations?

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Introduction

TFP largely accounts for cross-country GDP per capita di�erences.(e.g. Caselli, 2005: capital + human capital explains <50% crosscountry income per capita)

Part of these TFP di�erences have been attributed to:

• Larger dispersion of marginal product of capital and laboracross �rms in developing economies, misallocation.

I Evidence found in many countries: Hsieh & Klenow (2009),Busso, Madrigal & Pages (2012).

I For example: reducing dispersion across manufacturing plantsin Mexico to level of US implies a TFP gain of approx. 50%.

• Lower growth of productivity at the �rm level (Hsieh &Klenow, 2014).

What models (and frictions) can explain these observations?

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Introduction

TFP largely accounts for cross-country GDP per capita di�erences.(e.g. Caselli, 2005: capital + human capital explains <50% crosscountry income per capita)

Part of these TFP di�erences have been attributed to:

• Larger dispersion of marginal product of capital and laboracross �rms in developing economies, misallocation.

I Evidence found in many countries: Hsieh & Klenow (2009),Busso, Madrigal & Pages (2012).

I For example: reducing dispersion across manufacturing plantsin Mexico to level of US implies a TFP gain of approx. 50%.

• Lower growth of productivity at the �rm level (Hsieh &Klenow, 2014).

What models (and frictions) can explain these observations?

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Introduction

What frictions can generate misallocation?

• Financial constraints: �rms without su�cient collateral are notable to produce with optimal level of capital, then mg. productof capital is not equalized across �rms.

• However: models of �nancial constraints and �rm dynamicsgenerate modest TFP losses through misallocation relative todata (4-5% in Midrigan & Xu, 2013).

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Introduction

What frictions can generate misallocation?

• Financial constraints: �rms without su�cient collateral are notable to produce with optimal level of capital, then mg. productof capital is not equalized across �rms.

• However: models of �nancial constraints and �rm dynamicsgenerate modest TFP losses through misallocation relative todata (4-5% in Midrigan & Xu, 2013).

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Introduction

Additional channel through which �nancial constraints a�ect TFP:

• Financial constraints a�ect incentives to invest inknowledge/intangible capital: if entrepreneur is not able toproduce at optimal scale (e.g. optimal level of physical capital)will reduce investments in productivity,

• then �nancial constraints reduce the growth of productivity atthe �rm level, reducing aggregate TFP.

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Introduction

Additional channel through which �nancial constraints a�ect TFP:

• Financial constraints a�ect incentives to invest inknowledge/intangible capital: if entrepreneur is not able toproduce at optimal scale (e.g. optimal level of physical capital)will reduce investments in productivity,

• then �nancial constraints reduce the growth of productivity atthe �rm level, reducing aggregate TFP.

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Introduction

To analyze this mechanism we can extend previous modelsw/endogenous �rm productivity accumulation:

• �rms make investments to improve productivity every period(Pakes & McGuire, 1994; Klette & Kortum, 2004), �rmproductivity evolves stochastically,

• the model can tell us how much of the di�erences in theproductivity growth of �rms and aggregate TFP acrosscountries is accounted for by �nancial constraints.

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Introduction

To analyze this mechanism we can extend previous modelsw/endogenous �rm productivity accumulation:

• �rms make investments to improve productivity every period(Pakes & McGuire, 1994; Klette & Kortum, 2004), �rmproductivity evolves stochastically,

• the model can tell us how much of the di�erences in theproductivity growth of �rms and aggregate TFP acrosscountries is accounted for by �nancial constraints.

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Quantitative Model: Economics Forces at Work

In the model the following mechanisms come into play:

• �nancial constraints lower the incentives of entrepreneurs toinvest in productivity (entrepreneur will not be able to produceat optimal level and reap bene�ts of higher productivity),

• lower wages lead to lower ability individuals entering theeconomy (a standard result since Lucas, 1978).

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Quantitative Model: Outline

Main elements of the model:

• occupational choice: entrepreneur or worker,

• �nancial constraints,

• investment in knowledge capital (stochastic),

• small open economy,

• (extended model with productivity shocks, informal sector inpaper).

Builds upon Lucas (1978), Hopenhayn (1992), Pakes & McGuire(1994), Klette & Kortum (2004), Buera, Kaboski & Shin (2011).

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Production Technology

Entrepreneur w/ability ϕ (�xed) has access to the technology:

q = (ϕ n)1−ν f (k, l)ν

where:

• q is production of �nal good,

• f (k , l) = kα l1−α, ν ∈ (0, 1) decreasing returns-to-scale,

• ϕ is permanent ability of the entrepreneur, distribution h(ϕ),

• knowledge capital n, accumulated through investment ininnovation good x .

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Innovation Technology

• Every period knowledge capital n can increase:

P(n′ = n (1+ ∆) | n, x) = (1− γ)(1− λ) a (x/n)1+ a (x/n)

+ γ

• Probability of a decrease (bad shock) in knowledge capital:

P(n′ = n/(1+ ∆) | n, x) = (1− γ) λ

1+ a (x/n)

• With remaining probability, remains unchanged.

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Innovation Technology

• Every period knowledge capital n can increase:

P(n′ = n (1+ ∆) | n, x) = (1− γ)(1− λ) a (x/n)1+ a (x/n)

+ γ

• Probability of a decrease (bad shock) in knowledge capital:

P(n′ = n/(1+ ∆) | n, x) = (1− γ) λ

1+ a (x/n)

• With remaining probability, remains unchanged.

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Workers

s = {ϕ, nw , b}, problem of worker is a savings b′ ≥ 0 decision:

vw (s) = max{b′≥0}

u(c) + β (1− µ) ∑{z ′}

Q(z ′) v(s ′)

s.t. c + b′ = w + (1+ r) b

and occupation decision with random opportunity z ∈ {0, 1}:

v(s) = max{ve(z ϕ, nw , b), vw (s)}

initial level of knowledge capital available to the worker is nw .

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Workers

s = {ϕ, nw , b}, problem of worker is a savings b′ ≥ 0 decision:

vw (s) = max{b′≥0}

u(c) + β (1− µ) ∑{z ′}

Q(z ′) v(s ′)

s.t. c + b′ = w + (1+ r) b

and occupation decision with random opportunity z ∈ {0, 1}:

v(s) = max{ve(z ϕ, nw , b), vw (s)}

initial level of knowledge capital available to the worker is nw .

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Entrepreneurs

s = {ϕ, n, b}, entrepreneurs choose b′ ≥ 0 and x ≥ 0 to max:

ve(s) = u(c) + β (1− µ) ∑{n′}

P(n′ | n, x) max{vw (s ′), ve(s ′)}

subject to budget constraint:

c + b′ = π(s)− x + (1+ r) b

pro�ts are π(s) = q − (δ + r) k − w l subject to constraint (nextslide): k ≤ k(s).

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Entrepreneurs

s = {ϕ, n, b}, entrepreneurs choose b′ ≥ 0 and x ≥ 0 to max:

ve(s) = u(c) + β (1− µ) ∑{n′}

P(n′ | n, x) max{vw (s ′), ve(s ′)}

subject to budget constraint:

c + b′ = π(s)− x + (1+ r) b

pro�ts are π(s) = q − (δ + r) k − w l subject to constraint (nextslide): k ≤ k(s).

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Financial Enforcement Constraint

In the case of no-default the entrepreneur receives ND:

max{ l }

q − w l − (r + δ) k − x + (1+ r) b

while in the case of default the entrepreneur would receive D:

max{ l }

(1− ψ) (q − w l + (1− δ) k)− x

A capital level is enforceable if it satis�es ND≥D, implying abound k(s) on capital rental (a reduced form of capturingdi�erences in property rights/creditor protection).

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Predetermined Parameters.

parameter value description

β (1− µ) 0.92 e�ective discount factorσ 1.50 risk aversionr 0.04 interest rate (small open economy)

ν 0.85 span-of-controlα 1/3 income share of capitalδ 0.08 capital depreciation rate

a 3.00 innovation technologyλ 0.70 innovation technology

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Calibrated Parameters - US Moments.

parameter symbol value

exogenous exit rate µ 0.05�rm entry probability ϑ 0.04Pareto dist. θ 4.34innovation technology γ 0.24initial knowledge capital nw/n 1.91size innovation steps ∆ 0.38

target statistics data model

death rate large �rms 0.05 0.05total �rm entry/exit rate 0.10 0.11std. deviation growth rates 0.25 0.25relative size �rms [20-25]/[1-5] years 2.48 2.46employment at �rms w/50+ workers 0.69 0.60knowledge capital investment/total output 4.40 3.83

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Quantitative Exercise

We lower ψ to target the ratio of private credit/output in anemerging economy of 20%.

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Main Results.

statistics US EE

weighted �rm productivity 1.00 0.80TFP 1.00 0.92aggregate output 1.00 0.66

�rm productivity [20-25]/[1-5] years 2.61 1.26

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Final Comments

• We have explored a new channel through which �nancialconstraints have an impact on aggregate TFP: they distort theincentives to invest in productivity at the �rm level.

• Extended model with informal sector (low productivity and lowgrowth �rms w/no access to credit) and forthcoming:quantitative relevance of size dependent distortions vs.�nancial constraints.

• Buera, Kaboski and Shin (2015): more research is needed inendogenous entrepreneurial productivity!

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